MA321-7-SP-CO:
Applied Statistics
2020/21
Mathematics, Statistics and Actuarial Science (School of)
Colchester Campus
Spring
Postgraduate: Level 7
Current
Sunday 17 January 2021
Friday 26 March 2021
15
16 July 2020
Requisites for this module
(none)
(none)
(none)
(none)
(none)
MSC G30412 Data Science,
MSC G30424 Data Science,
MSC G304PP Data Science with Professional Placement,
DIP G30009 Statistics,
MSC G30012 Statistics,
MPHDG30048 Statistics,
PHD G30048 Statistics,
MPHDG30448 Data Science,
PHD G30448 Data Science
This module covers four application areas of statistics: multivariate methods, support vector machines, demography and epidemiology, and sampling (PG module 5 of the syllabus of the Royal Statistical Society).
The aim of the module is to foster statistical thinking and create data scientists that have both theoretic knowledge and application skills.
On completion of the course students should be able to:
- Understand and to apply multivariate methods;
- Assess the results of discriminant analysis, principal components, cluster analysis and multivariate analysis of variance;
- Understand and to apply demographical and epidemiological methods;
- Understand and to use the notion of support vector machines, with applications to classification;
- Understand and to apply sampling methods.
Syllabus
Multivariate methods
Vectors of expected values. Covariance and correlation matrices. Discriminant analysis, choice between two populations, calculation of discriminant function, and probability of misclassification, test and training samples, leave-one-out and k-fold cross-validation, idea of extension to several populations. Principal components; definition, interpretation of calculated components, use in regression. Cluster analysis, similarity measures, single-link and other hierarchical methods, k-means. Informal approaches to checking for multivariate Normality. Tests and confidence regions for multivariate means.
Support vector machines
Maximal margin classifiers. Hyperplanes. Classification using a separating hyperplane. Non-separable case. Support vector classifiers. Support vector machines; classification with non-linear decision boundaries. The support vector machine. Support vector machines with more than two classes; one-versus-one and one-versus-all classification. Relationship to logistic regression.
Demography and epidemiology
Population pyramids. Life tables. Standardised rates (e.g. mortality). Incidence and prevalence. Design and analysis of cohort (prospective) studies. Design and analysis of case-control (retrospective) studies. Confounding and interaction. Matched case control design and analyses, using McNemar's test. Causation. Relative risk. Odds ratio. Estimation and confidence intervals for 2x2 tables. Mantel-Haenszel procedure. Sensitivity, specificity, ROC curves, positive predictive value, negative predictive value.
Sampling
Census and sample survey design. Target and study populations, uses and limitations of non-probability sampling methods, sampling frames, sampling fraction. Simple random sampling. Estimators of totals, means and proportions; bias. Estimated standard errors, confidence intervals and precision. Sampling fraction and finite population correction. Ratio and regression estimators. Stratified random sampling. Estimators of totals, means and proportions; bias. Estimated standard errors, confidence intervals and precision. Cost functions. Proportional and optimal allocations. Limitations of stratified sampling. One-stage cluster sampling. Estimators for totals, means and proportions with equal cluster sizes and with different cluster sizes. Estimated standard errors, confidence intervals and precision. Link with systematic sampling. Description of two-stage sampling and of multi-stage sampling. Limitations.
Teaching will be delivered in a way that blends face-to-face classes, for those students that can be present on campus, with a range of online lectures, teaching, learning and collaborative support.
- James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert. (2013) An introduction to statistical learning: with applications in R, New York: Springer. vol. Springer texts in statistics
The above list is indicative of the essential reading for the course. The library makes provision for all reading list items, with digital provision where possible, and these resources are shared between students. Further reading can be obtained from this module's reading list.
Assessment items, weightings and deadlines
| Coursework / exam |
Description |
Deadline |
Coursework weighting |
| Coursework |
Assignment 1 |
|
25% |
| Coursework |
Assignment 2 |
|
75% |
| Exam |
Main exam: 240 minutes during Summer (Main Period)
|
Exam format definitions
- Remote, open book: Your exam will take place remotely via an online learning platform. You may refer to any physical or electronic materials during the exam.
- In-person, open book: Your exam will take place on campus under invigilation. You may refer to any physical materials such as paper study notes or a textbook during the exam. Electronic devices may not be used in the exam.
- In-person, open book (restricted): The exam will take place on campus under invigilation. You may refer only to specific physical materials such as a named textbook during the exam. Permitted materials will be specified by your department. Electronic devices may not be used in the exam.
- In-person, closed book: The exam will take place on campus under invigilation. You may not refer to any physical materials or electronic devices during the exam. There may be times when a paper dictionary,
for example, may be permitted in an otherwise closed book exam. Any exceptions will be specified by your department.
Your department will provide further guidance before your exams.
Overall assessment
Reassessment
Module supervisor and teaching staff
Dr Fanlin Meng, email: fanlin.meng@essex.ac.uk.
Dr Fanlin Meng & Dr Stella Hadjiantoni
Dr Fanlin Meng (fanlin.meng@essex.ac.uk), Dr Stella Hadjiantoni (stella.hadjiantoni@essex.ac.uk)
Yes
No
No
Prof Fionn Murtagh
University of Huddersfield
Professor of Data Science
Available via Moodle
Of 2553 hours, 0 (0%) hours available to students:
2553 hours not recorded due to service coverage or fault;
0 hours not recorded due to opt-out by lecturer(s).
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